Notice that the \(L_1\)  norm term in Problem (REF ) is not smooth. One way to solve the optimization problem is to use the stochastic subgradient descent (SSGD) algorithm [1]}. Let \(F\left( S \right) = E\left[ {f\left( S \right)} \right] = E\left[ {\sum \limits _{t = 1}^T {{C_t}\left( S \right)} } \right]\) and \(G\left( S \right) = \lambda {\left\Vert  S \right\Vert _1}\) . The iteration of the SSGD algorithm takes the form
\({S_{k + 1}} = {S_k} - {t_k}\left( {\nabla f\left( {{S_k}} \right) + {\xi _k}} \right),\) 
